Pages

Recent Posts

Wednesday, February 21, 2018

Simple Inflation Breakeven Versus Economic Breakeven

In the analysis of inflation-linked bonds, we quite often refer to the inflation breakeven rate. The usual way of thinking about this is to say that this is the rate of inflation which results in the inflation-linked bond having the same return as a conventional bond. However, we technically need to have two definitions: the economic inflation breakeven, and the simple inflation breakeven. The simple inflation breakeven is just the spread between the inflation-linked bond and a similar maturity conventional (nominal) bond. Although there can be a wedge between the concepts, the simple inflation breakeven will tend to be close to the economic breakeven.

This article is meant to be worked into my upcoming Inflation Breakeven Analysis report, although it contains background information that appears in other sections.

Although one could try to define the economic breakeven for a linker relative to a particular nominal bond, such a definition has some risks. It is much cleaner to define the economic breakeven versus an entire nominal discount curve. This way we have a sensible discount factor for every inflation-linked cash flow. This is not the case for matching against a particular nominal bond. The maturity dates may not line up, and it is unclear that a flat discount rate (the nominal bond yield) is useful, as the cash flow patterns of a linker and a conventional bond are different. (If inflation breakeven rates are positive, the inflation-linked bond will tend to look more like a zero coupon bond.)

We can then define the economic inflation breakeven as the extrapolated inflation rate that results in the inflation-linked bond being fairly priced on the nominal discount curve. If we are being careful, we should also take into account inflation seasonality, and so we are technically extrapolating seasonally-adjusted inflation, and then backing out the "seasonalised" equivalent of the series. (This is the reverse operation of the more standard seasonal adjustment procedure.)

The simple inflation breakeven is the spread of a "similar" maturity conventional bond (the comparator) over the quoted yield (real yield) of the inflation-linked bond. (I assume the Canadian model here.) The simple inflation breakeven is quoted in percent, not basis points.

Since we can have two conventional bonds with "similar" maturities trading after different yields, the simple inflation breakeven varies based on comparator. Things can get quite messy for short-dated bonds, as a few month mismatch between the conventional maturity and the linker maturity can result in a large seasonal adjustment factor between the two maturity dates.

However, if we are looking at fitted bond yields (e.g., the Fed H.15 Report series), the simple breakeven is a good approximation of the economic breakeven.

Example

We start off with the nominal zero curve pictured above, with the zero rate rising from 4% to 6% at the 10-year tenor. A fixed income relative value specialist would likely point out that the above zero curve is implausible, but that is not a concern here.

(All calculations were done in Python in my "SimplePricers" package. The code is not meant for production purposes, but rather examples to illustrate how more complex pricers work. The code is available at: https://github.com/brianr747/SimplePricers, the results were generated by the file ex20180216_breakeven.py in the examples folder. The code used to generate the examples today used some shortcuts, but it is expected that these would not materially change the outcome. I have not had a great deal of time to validate the work, but the numbers appeared plausible.)

We will assume that all nominal bonds trade at fair value on the above zero curve.

We will start with a 10-year 4% annual coupon inflation-linked bond that is trading at par (hence a 4% real yield).

Using the simplification that inflation rises smoothly from the valuation date (and that there is no known information from CPI calculation lags), the economic inflation breakeven rate was 1.80%.

Meanwhile, I have two 10-year conventional bonds.

A 10-year par coupon (annual coupon) bond with a coupon of 5.81%. The simple inflation breakeven is 1.81%, a whopping 1 basis point deviation from the economic breakeven.

An old 8% 10-year (annual coupon) bond, which is trading at a yield of 5.76%, or a price of $116.64. (All numbers are rounded.) It is trading at a lower yield than the par coupon since it's cash flows are weighted more towards the front of the curve, where the zero rate is lower. The simple economic breakeven is 1.76%, 4 basis points away from the economic breakeven.

Obviously, the simple breakeven could get further out of line if the comparator is grossly mis-priced versus the zero curve.

If we then vary the coupon of the inflation-linked bond, we also see small changes. If we have a 2% coupon 10-year inflation-linked bond trading at the same real yield (4%), it has a price of $83.78. Since it has the same real yield, it would have the simple inflation breakeven rate as the 4% coupon bond. However, the economic inflation breakeven rate rises 5 basis points to 1.85%.

As can be seen, the standard practice of subtracting the fitted inflation-linked bond yield from a fitted nominal bond yield (both series being par coupon series) is going to give numbers that are in the ballpark of the true inflation breakeven for bonds that are trading near par, for sufficiently long maturities.

At shorter maturities, we would need to worry about the effects of seasonality and known information about the future path of the daily CPI index. For example, if we are calculating the inflation breakeven rate of a bond that matures in five weeks, while we know that the daily CPI index will rise very rapidly over the next three weeks because of an gasoline price spike in the last CPI report, the economic inflation breakeven rate may bear little resemblance to the spread between the inflation-linked bond yield and the yield on a 5-week nominal instrument.

(My example code ignores what is known about the daily CPI index when defining the economic breakeven inflation rate.)

No comments:

Post a Comment

Note: Posts may be moderated, and there may be a considerable delay before they appear.

Although I welcome people who disagree with me, please be civil.

Please note that my spam comment filter appears to dislike long "anonymous" posts. I get no warning about this, and only go through my "spambox" infrequently. The best bet it to keep comments short, and if you think the spam filter struck, let me know with a short comment.

Contact Form

Subscribe To

Navigation

Disclaimer/Privacy

See my "Disclaimer" page for my privacy policy as well as advertising affiliate information. Please note that I use Google Analytics, which tracks user data; you will need to look at their documentation to see what they do about privacy. This website also incorporates links that are part of the Amazon affiliate program (which includes the images of book covers); you will need to consult their websites to see what tracking information they use. This blog contains general discussions of economic and financial market trends for a general audience. These are not investment recommendations tailored to the particular needs of an investor. The author may discuss strategies which are wildly inappropriate for retail investors. Any mention of corporate securities are for illustrative purposes only; the author does not make recommendations to buy or sell such securities (and frankly, has no expertise to do so). No warranties are made with regards to the correctness of data or analysis, and some data may be under copyright protection of the original data provider. Past performance is not a predicton of future performance (which should make some bond bulls fairly nervous).